Question

The diagram shows a ray of light striking a plane mirror. What is the angle of incidence if the angle of incident ray and reflected ray is ${80^0}$?

A.\[{35^0}\]
B.${40^0}$
C.${70^0}$
D.${80^0}$

Answer 1

Hint: When any ray of light strikes the plane of the mirror the reflection takes place in the same angle that is angle of incidence is equal to angle of reflection.we can use this concept to solve this problem.

Complete step by step answer:
Given: The angle between incident ray and reflected ray = ${80^0}$
The angle which an incident line or ray makes with a perpendicular to the surface at the point of incidence is called angle of incidence.
The angle made by a reflected ray with a perpendicular to the reflecting surface is called angle of reflection.
When any ray of light strikes the plane of the mirror the reflection takes place in the same angle that is angle of incidence is equal to angle of reflection \[\angle {\rm{ }}i{\rm{ }} = {\rm{ }}\angle {\rm{ }}r\]………………………………………………………………………………….(i)
Where i = angle of incidence and r = angle of reflection
Hence,
\[\angle {\rm{ }}i{\rm{ }} + {\rm{ }}\angle {\rm{ }}r{\rm{ }} = {\rm{ }}80^\circ \]
\[\Rightarrow\angle {\rm{ }}r{\rm{ }} + \angle {\rm{ }}r\; = {80^0}\] ……………….(~ from(i) )
\[\Rightarrow2\left( {\angle {\rm{ }}r} \right){\rm{ }} = 80^\circ \]
\[\Rightarrow\angle {\rm{ }}r\; = \;80^\circ /2\]
\[\Rightarrow\angle {\rm{ }}r\; = \;\;40^\circ \]
Since angle of reflection and angle of incidence are equal for plane mirror,
 \[\angle {\rm{ }}i{\rm{ }} = {\rm{ }}\angle {\rm{ }}r\;\;\; = \;\;40^\circ \]
Therefore angle of incidence is equal to \[40^\circ\].

Therefore, Option (B) is the correct answer.

Note: The ratio of sine of incidence angle to sine of refraction angle is a constant term. Or we can say, the ratio of sine of reflected angle to sine of refraction angle is constant term. Reflection and refraction are different terms from each other.